Relative size can be represented qualitatively at the simplest level by the
qualitative relations: bigger, smaller, and equal to. In the ASSF system,
relative size of objects within a scene, features within subparts, and
subparts within objects, are all expressed in terms of the lengths of
different types of axes.

The two axes which are most often used as a reference for relative size are
the major and minor axes of each distinct shape; such shapes can
be either a complete object, a subpart, or an imple. Local relative size is
expressed by comparing a given dimension to these axes. Five qualitative
values are immediately available: there are three qualitative ranges (less
than the minor axis, between the minor and major axes, and greater than the
major axis) and two distinguished points (major and minor).

Section 4.1.4 above points out the ways in which this
approach is unsatisfactory, and also some partial solutions. One partial
solution is to further subdivide the quantity space, so that it is possible to
make qualitative distinctions between sizes that are closer in magnitude. I
have done this by introducing further ``distinguished'' points at one half and
one quarter of the major and minor axis lengths. This results in a quantity
space with six distinguished points and seven qualitative ranges, which can be
used to construct a satisfactory representation of quite complex objects
(especially where local complexity is treated using a local set of imple
axes), but which still suffers from the limitations described in
section 4.1.4 if there are essentially equal sizes
that are accidentally separated into different quantity space ranges.

Individual features are measured along their own axis, which is usually a
straight line between the points at either end of the feature. This is true
of straight and curved edges, and also of imples, which are measured along the
waist where the imple meets another convex part. Secondary axis measurements
are used to define the shape of an imple, by specifying the size of imple
major and minor axes relative to the axes of the main shape. All of these
feature sizes are described by comparing them to the local quantity space
defined from the major and minor axes of the main shape.